Simplify square root of 54y^12

$\sqrt{54 y^{12}}$

Step 1

Rewrite $54 y^{12}$ as ${(3 y^{6})}^{2} \cdot 6$ .

Factor $9$ out of $54$ .

$\sqrt{9 (6) y^{12}}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 6 y^{12}}$

Rewrite $y^{12}$ as ${(y^{6})}^{2}$ .

$\sqrt{3^{2} \cdot 6 {(y^{6})}^{2}}$

Move $6$ .

$\sqrt{3^{2} {(y^{6})}^{2} \cdot 6}$

Rewrite $3^{2} {(y^{6})}^{2}$ as ${(3 y^{6})}^{2}$ .

$\sqrt{{(3 y^{6})}^{2} \cdot 6}$

Step 2

Pull terms out from under the radical.

$3 y^{6} \sqrt{6}$